Surface-limited vapor solvent growth of crystals

Abstract

A general analysis is presented of surface reaction limitations in a vapor solvent system. A previous treatment of a multicomponent multireaction vapor diffusion limited system is extended to include finite supersaturations in the neighborhoods of the growing deposit and the etching source. The appropriate natural definitions of supersaturations are found to be in agreement with the usual conventions of irreversible thermodynamics. A more detailed connection between the supersaturations above a growing crystal and the growth rate of the crystal is developed by means of an extension of the crystal growth theory of Burton, Cabrera, and Frank to apply to a multiple species multireaction vapor solvent system. It is found, at least in the limit of low supersaturations, that the flux of any particular species to the surface may be treated in terms of the formalism developed by Burton, Cabrera, and Frank for a monatomic crystal-monatomic vapor system, except that some of the parameters which characterize the process, e.g., diffusion length on the surface, lifetime on the surface, etc., have more phenomenological character. Relationships between the fluxes of different species are developed in the same manner as in the previously treated vapor diffusion limited system. Quantitative calculation of the important parameters is apparently impossible in our present state of knowledge of surface processes. Qualitatively, we expect surface diffusion effects to be far more important than in simple crystal-vapor systems. Other effects, however, are also expected to be important in vapor solvent systems, e.g., "kink-reaction" limitations, impurity effects, etc. Disentanglement of these several processes is an unsolved problem and it is concluded that detailed quantitative understanding of surfacelimited crystal growth in a vapor solvent system is presently out of reach.